Phase Transitions and Renormalization Group
By (author) Jean Zinn-Justin
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Phase Transitions and Renormalization Group by Jean Zinn-Justin
Book DescriptionThis work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. We will assign this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance, beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process, that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. We thus discuss the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, we construct a general functional renormalization group, which can be used when perturbative methods are inadequate.
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Book DetailsISBN: 9780199227198
(250mm x 170mm x 25mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 5-Jul-2007
Country of Publication: United Kingdom
Books By Author Jean Zinn-Justin
Phase Transitions and Renormalization Group, Paperback (January 2013)
The renormalization group is one of most important theoretical concepts that has emerged in physics during the twentieth century. It explains important properties of fundamental interactions at the microscopic scale, as well as universal properties of continuous macroscopic phase transitions.
Path Integrals in Quantum Mechanics, Paperback (July 2010)
Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.
Quantum Field Theory and Critical Phenomena, Hardback (June 2002)» View all books by Jean Zinn-Justin
This is the first book on Quantum Field Theory which emphasizes the common aspects of particle physics and the theory of critical phenomena. This new fourth edition is completely revised, with more than 50% new material added to the OUP classic.
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Author Biography - Jean Zinn-Justin
Professor Jean Zinn-Justin Head of Department, Dapnia, CEA/Saclay, France
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